Obfuscating Conjunctions under Entropic Ring LWE
Author(s)Brakerski, Zvika; Vaikuntanathan, Vinod; Wee, Hoeteck; Wichs, Daniel
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We show how to securely obfuscate conjunctions, which are functions f(x[subscript 1], . . . , x[subscript n]) = ∧[subscript i∈I] y[superscript i] where I ⊆ [n] and each literal y[subscript i] is either just x[subscript i] or ¬x[subscript i] e.g., f(x[subscript 1], . . . , x_n) = x[subscript 1] ⊆ ¬ x[subscript 3] ⊆ ¬ x[subscript 7] · · · ⊆ x[subscript n−1]. Whereas prior work of Brakerski and Rothblum (CRYPTO 2013) showed how to achieve this using a non-standard object called cryptographic multilinear maps, our scheme is based on an “entropic” variant of the Ring Learning with Errors (Ring LWE) assumption. As our core tool, we prove that hardness assumptions on the recent multilinear map construction of Gentry, Gorbunov and Halevi (TCC 2015) can be established based on entropic Ring LWE. We view this as a first step towards proving the security of additional multilinear map based constructions, and in particular program obfuscators, under standard assumptions. Our scheme satisfies virtual black box (VBB) security, meaning that the obfuscated program reveals nothing more than black-box access to f as an oracle, at least as long as (essentially) the conjunction is chosen from a distribution having sufficient entropy.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16
Association for Computing Machinery
Brakerski, Zvika, et al. "Obfuscating Conjunctions under Entropic Ring LWE." Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16, 14-17 January, 2016, Cambridge, MA, ACM Press, 2016, pp. 147–56.
Author's final manuscript